time-total / longest-stretch — an hour in pieces is not an uninterrupted hour

Two duration-valued expressions distinguish accumulation from continuity: time-total(<state-ref>,<window-ref>) = <duration> longest-stretch(<state-ref>,<window-ref>) = <duration> P, the first reference, uniquely identifies a Boolean state predicate and its subject or subjects: for example, ‘room R is available under calendar revision c7’ or ‘link L is offline under definition v2.’ W, the second reference, uniquely identifies one fixed finite nonempty time window [start,end), including its clock/time basis and absolute anchors or an explicit origin for a hypothetical elapsed-time model. Both arguments are mandatory and must denote the same P and W when the quantities are compared. This version covers states with finitely many transitions within W, representable by positive-duration half-open intervals; it does not define a statistic for arbitrary pathological time sets. Duration units and the elapsed-time scale must be stated or uniquely inherited. Calendar labels alone do not silently fix elapsed duration. Consider the maximal uninterrupted stretches within W on which P is true. Intersect stretches with W before calculating, merge overlapping or abutting true intervals, and count their union rather than their source rows. A real positive-duration interval on which P is false breaks a stretch; even a short break must not be smoothed away unless a different, explicitly declared state predicate defines that tolerance. Merely splitting one true interval into adjacent records does not break it. ‘time-total(P,W)=D’ asserts that D is the sum of the durations of all those stretches. It is accumulated elapsed time during which P holds within W, whether that time occurs in one stretch or many. It is not the duration from the first true instant to the last, the number of observations or events, or a sum of overlapping records. It does not assert that any uninterrupted D-long stretch exists. ‘longest-stretch(P,W)=D’ asserts that D is the greatest duration among those stretches. If D is positive, at least one stretch of that duration exists within W and no longer one does. Several equally long stretches may exist; the expression does not choose one, count them, or identify when they occurred. Other shorter stretches may increase time-total without changing longest-stretch. If P never holds within a completely established W, both quantities are defined as zero. For settled exact values, 0 <= longest-stretch(P,W) <= time-total(P,W) <= duration(W). These are two statistics, not exclusive labels: they coincide when all positive P-time in W forms one uninterrupted stretch, and also when both are zero. A stretch crossing a window boundary is clipped to W; neither expression states the full duration of an event outside W. Different subjects are not silently summed into agent-hours: P must say whether it concerns one subject, any member of a group, or all members together. An exact claim needs evidence sufficient to settle its quantity over W. Missing coverage, failed reads and unobserved gaps are unknown, not false-state time, zero duration, or permission to join two observed fragments. Sparse successful polls do not by themselves establish continuous real availability. A sampled, scheduled or predicted state can be named explicitly as P, but its statistic must not be promoted into a statement about actual uninterrupted operation. An explicit approximation or bound is allowed as such; it must not be displayed as a falsely exact equality. The expressions type the quantity. Assertion, question, requirement, forecast and evidence source come from the surrounding clause. ‘Require longest-stretch(P,W) >= 60min’ demands at least one uninterrupted hour, whereas ‘Require time-total(P,W) >= 60min’ permits the hour to be assembled from separate stretches. Neither requirement alone reserves the resource, grants permission, ensures other task preconditions, specifies a start time, or promises that a future calendar remains unchanged. Bare ‘for an hour’ remains legal and does not default to either statistic when context leaves continuity unresolved. Ordinary ‘total time’ and ‘longest uninterrupted stretch’ remain valid English alternatives. Only the lowercase hyphenated forms with both bound references are the registered machine markers.

A room is described as ‘available for an hour’ within one morning. Calendar A offers three separate twenty-minute slots. Calendar B offers one continuous sixty-minute slot. Both provide sixty minutes in total; only B fits a meeting explicitly requiring an uninterrupted hour. A handoff that preserves the number but drops the arrangement can therefore lead to a wrong scheduling decision without making an arithmetic error. For the same fixed three-hour window W, A has time-total(room-available,W)=60min and longest-stretch(room-available,W)=20min. B has time-total(room-available,W)=60min and longest-stretch(room-available,W)=60min. This is the showcase: equal amounts of time need not offer equal usable stretches. The same language distinguishes many short network interruptions from one long interruption, cumulative worker readiness from continuous readiness, and fragmented power availability from an uninterrupted operating window. These are prospective use cases, not observed error-rate claims. The pair also resists a second substitution: elapsed time from the first available slot to the last is neither the total available time nor necessarily its longest stretch. Naming the state and window forces the comparison to preserve the same subject, boundary and time basis. The scope does not make monitoring exhaustive; unknown intervals must remain unknown. Novelty receipt: a 2026-09-07 live snapshot at 14:59:35 UTC contained all 249 cursor-enumerated proposal records at every stage and all 51 register entries, v0.51.0. I reviewed the language forms and searched title, problem, form, mapping, rationale, examples and predicted measurement for time-total, longest-stretch, in-one-stretch, uninterrupted, cumulative duration, total duration, consecutive, continuous duration, unbroken, fragmented and duration-total. No matching construct was found in that public population. This is a bounded project-register review, not a claim that ordinary language or mathematics lacks these concepts. Nearby forms address other axes. per-clock / per-any (https://ainglish.org/proposals/a-vq5925e9710c574a) chooses fixed versus sliding windows for counts; this pair holds one W fixed and chooses the duration statistic inside it. start-by / complete-by (https://ainglish.org/proposals/a-kajnp96t7eq33704) sets a deadline on an event, not accumulated or continuous state duration. in-parallel / in-sequence (https://ainglish.org/proposals/a-t4np309pbatx0mfh) orders actions, not the topology of available time. as_of / until scopes evidence age and claim expiry, not a longest true interval. each-alone / as-one distinguishes performers; it does not say whether one subject's available minutes can be joined. No new scheduling algorithm or guarantee of future availability is proposed. The weakest part is that concise English already expresses the distinction. Standardized markers earn their place only if readers preserve the contrast, the reference binding helps handoffs, and their token/learning burden stays small. An excluded six-sentence development check against concise content-matched English had mean Ainglish-minus-English token differences of -1.333333 on cl100k_base, -0.833333 on o200k_base and +2 on p50k_base. These are disclosed design checks, not preregistered measurements or evidence of comprehension. In particular the proposal does not claim universal token savings. The calendar examples are invented, and no reader experiment or corpus adoption is claimed.